How do you clean a lip piercing besides nonalcoholic mouthwash?

Hydrogen Peroxide: Hydrogen peroxide is always a good alternative.

Take It Out: Removing the piercing is the only true way to clean the area. Since that's probably not an option, you're on the right track with non-alcoholic mouthwash. Diluted peroxide works pretty well too, if you can handle the taste. Jast as important as cleanliness is not playing with the piercing. Chewing on it, or having it clank against your teeth will cause damage over time. Broken teeth are common.